our main graph: average error rate - number of devices

device error rate: zipf distribution with parameter 2, after getting the distribution, we divide it by 100

data size: zipf distribution with parameter 2

data ratio: 0.5

To be more specific:

small,相对于greedy提升: 0.4924601179876383
small,相对于SLSQP提升: 0.21309760822744192
medium,相对于greedy提升: 0.3892033319239571
medium,相对于SLSQP提升: 0.13570298910442993
large,相对于greedy提升: 0.3000516497088584
large,相对于SLSQP提升: 0.19056149281682314
全局,相对于greedy最小提升： 0.15927065097312595
全局,相对于greedy最大提升： 0.7265050439693782
全局,相对于greedy平均提升： 0.38896538144376736
全局,相对于SLSQP最小提升： -0.2140927362917622
全局,相对于SLSQP最大提升： 0.39576960107326214
全局,相对于SLSQP平均提升： 0.1457862136147851

average error rate performance - data ratio

device error rate: zipf distribution with parameter 2, after getting the distribution, we divide it by 100

data size: zipf distribution with parameter 2

online device numbers: 25

To be more specific:

small,相对于greedy提升: 0.4235255656854579
small,相对于SLSQP提升: 0.2561197749894512
medium,相对于greedy提升: 0.4540778865118285
medium,相对于SLSQP提升: 0.1632340758167984
large,相对于greedy提升: 0.28726265423512476
large,相对于SLSQP提升: 0.15507535804171002
全局,相对于greedy最小提升： -0.009210402111178045
全局,相对于greedy最大提升： 0.8099652865113203
全局,相对于greedy平均提升： 0.37818609735323583
全局,相对于SLSQP最小提升： -0.18115725016794756
全局,相对于SLSQP最大提升： 0.5033772946525363
全局,相对于SLSQP平均提升： 0.14579754068502154

average error rate performance - data ratio

device error rate: F distribution with parameter (1,1), after getting the distribution, we divide it by 5

data size: F distribution with parameter (1,1)

online device numbers: 25

To be more specific:

small,相对于greedy提升: 0.4557158206215211
small,相对于SLSQP提升: 0.3042362559022756
medium,相对于greedy提升: 0.3531324977932644
medium,相对于SLSQP提升: 0.03842385915661154
large,相对于greedy提升: 0.16787394885166534
large,相对于SLSQP提升: 0.17094966576014922
全局,相对于greedy最小提升： -0.06737339897489557
全局,相对于greedy最大提升： 0.7292001275903853
全局,相对于greedy平均提升： 0.30980407506510177
全局,相对于SLSQP最小提升： -0.30664719957326914
全局,相对于SLSQP最大提升： 2.0115336285056085
全局,相对于SLSQP平均提升： 0.23965262866008455

average error rate performance - data ratio

device error rate: uniform distribution on [0,0.2]

data size: uniform distribution on [0,1]

online device numbers: 25

To be more specific:

small,相对于greedy提升: 0.3995817834144879
small,相对于SLSQP提升: 0.39861529241831656
medium,相对于greedy提升: 0.09101018896032653
medium,相对于SLSQP提升: 0.1889016229069118
large,相对于greedy提升: -0.011293527240038539
large,相对于SLSQP提升: 0.019619432205150507
全局,相对于greedy最小提升： -0.04901354118315896
全局,相对于greedy最大提升： 0.5304155300629732
全局,相对于greedy平均提升： 0.14266018081642892
全局,相对于SLSQP最小提升： -0.04957348124029826
全局,相对于SLSQP最大提升： 0.9496724439966612
全局,相对于SLSQP平均提升： 0.21186058079253586

best error rate performance upon different distributions

For uniform distribution, the device error ranges are:

• [0,1] / 5
• [1,2] / 5
• [2,3] / 5

and the data size ranges are:

• [0,1]
• [1,2]
• [2,3]

For F distribution, the device error ranges are:

• (1,1) / 5
• (8,3) / 5
• (20,20) / 5

and the data size ranges are:

• (1,1)
• (8,3)
• (20,20)

For zipf distribution, the device error ranges are:

• 1.5 / 100
• 2 / 100
• 3 / 100

and the data size ranges are:

• 1.5
• 2
• 3

data ratio: 0.5

online device number: 25

To be more specific:

uniform分布,small,相对于greedy提升: 0.43876329007451603
uniform分布,small,相对于SLSQP提升: 0.4381275804290543
uniform分布,medium,相对于greedy提升: 0.163567393118934
uniform分布,medium,相对于SLSQP提升: 0.42395981459081417
uniform分布,large,相对于greedy提升: 0.246786386060319
uniform分布,large,相对于SLSQP提升: 0.11776952907384786
f分布,small,相对于greedy提升: 0.31088498816749305
f分布,small,相对于SLSQP提升: 0.5055932633845275
f分布,medium,相对于greedy提升: 0.5621499089885922
f分布,medium,相对于SLSQP提升: 0.6721712077881525
f分布,large,相对于greedy提升: 0.7789260926492565
f分布,large,相对于SLSQP提升: 0.8417459536941804
zipf分布,small,相对于greedy提升: 0.9434280176926076
zipf分布,small,相对于SLSQP提升: 0.8122455206093158
zipf分布,medium,相对于greedy提升: 0.5263154798640055
zipf分布,medium,相对于SLSQP提升: 0.5263154798640055
zipf分布,large,相对于greedy提升: 0.4808435675699952
zipf分布,large,相对于SLSQP提升: 0.5604893085341159

best error rate performance upon different distributions in device error rate but fix data distribution on (1,1) F distribution

the setting is the same as figure 5 except that data distribution is fixed

uniform分布,small,相对于greedy提升: 0.5755465529129367
uniform分布,small,相对于SLSQP提升: 0.7665102839860015
uniform分布,medium,相对于greedy提升: 0.299096818222461
uniform分布,medium,相对于SLSQP提升: 0.5320995997114417
uniform分布,large,相对于greedy提升: 0.0976878089679025
uniform分布,large,相对于SLSQP提升: 0.10301065472833051
f分布,small,相对于greedy提升: 0.5229756838232974
f分布,small,相对于SLSQP提升: 0.5229756838232974
f分布,medium,相对于greedy提升: 0.3632245007158276
f分布,medium,相对于SLSQP提升: 0.3632245007158276
f分布,large,相对于greedy提升: 0.4135137935871781
f分布,large,相对于SLSQP提升: 0.0
zipf分布,small,相对于greedy提升: 0.9448415531793901
zipf分布,small,相对于SLSQP提升: 0.9192489653806374
zipf分布,medium,相对于greedy提升: 0.6923721474472584
zipf分布,medium,相对于SLSQP提升: 0.6923721474472584
zipf分布,large,相对于greedy提升: 0.5446353510058206
zipf分布,large,相对于SLSQP提升: 0.0

time used by each methods

the slowest one is SLSQP, the middle one is ranRFL, and the fastest one is GDS

through import raw data to csv in Excel, you can see it clearly

To be more specific: 这个表描述了算法运行时间随侯选设备数的变化关系，我们的算法在时间性能上优于SLSQP算法，劣于贪心算法，但随候选设备数增大，我们的算法运行时间仍在合理、可控的范围内

raw data:

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